Stroessner, 93, died of an infection caused by the pneumonia he developed after having an operation for a hernia last month, according to a doctor at Brasilia's Santa Luzia hospital.
"He was surrounded by his entire family," said Alfredo "Goli"
Stroessner, the former general's grandson and a leader of the governing Colorado Party, which supported the dictatorship.
"He died in absolute tranquility."
Stroessner lived in Brazil since he was ousted from Paraguay in a 1989 military coup, and was hospitalised in late July.
His grandson hailed him as a man "who profoundly loved his country ... a great Paraguayan."
But Senator Domingo Laino, once a leading opponent of the military dictatorship, said the former strongman would be remembered as "one of the bloodiest Latin American dictators of the 20th century".
Stroessner's rule was among the most brutal in the history of a country plagued by considerable bloodshed since its independence in 1811.
At least 1,000 opponents were abducted and presumed killed.
Opponents of the dictatorship put the number of dead at 3,000. In addition, some two million Paraguayans fled the country under
Stroessner.
"He was a ruthless, intolerant man," said Senator Laino, once considered the most prominent opponent of the dictatorship and now an opposition senator.
"He did not allow any criticism, he committed atrocious crimes," said Mr Laino, who was tortured and later exiled during the dictatorship after writing a book critical of Stroessner.
Stroessner had also drawn international criticism for granting asylum to Nazi war criminals, including Josef Mengele, the infamous Angel of Death at the Auschwitz concentration camp.
After rising to power in a 1954 coup, Stroessner, the son of a
Bavarian brewer and a Paraguayan woman, clung to power for 34 years winning eight rigged elections and drawing Cold War support from the United States.
He fostered a cult of personality, with streets, squares, hospitals, schools and even entire cities bearing his name.
His court was stacked with civilians and military men, many of them involved in lucrative businesses such as drug trafficking and automobile smuggling.
In an impoverished and mostly rural country, his family amassed a fortune as he consolidated power. A former wife of one of his sons, Maria Eugenia Heikel, estimated the family fortune at Us$300 million.
Stroessner also created a politico-religious sect, still in existence, called People of God - referred to as Catholic, apostolic and Paraguayan - in which he was portrayed in rewritten psalms as having been sent by God.
A huge photograph of the general adorned the entrance of a People of God congregation resplendent with Old Testament paintings.
Highways were lined with signs with his image, and statues of him bore his beloved motto: "Peace and Progress with Stroessner".
His grandson said the former general had "no regrets".
"He acted in accordance with the canons of the Cold War; he acted in accordance with what world politics demanded at the time, and he did what he had to do at the time," he said.
After his February 3, 1989 ouster, the long-time dictator - dubbed the Tyrannosaurus - fled to exile in Brazil to avoid prosecution for human rights violations.
In recent years, he lived in a lakeside Brasilia mansion with one of his sons and, reportedly, with seven servants.
Paraguayan media said the strongman, once an imposing general who stood nearly two metres tall, suffered from cancer and had wasted away to just 45 kilos when he died.
Relatives said they had not decided yet whether to repatriate the body.
Victims of the dictatorship have said they would stage protests if the body was sent to Paraguay for burial.